1.28: Coordinate Geometry of a Triangle and Circle

4PM1/2/June/2019 — Question 8 · 11 marks

The point A\displaystyle A has coordinates (2,6)\displaystyle (2,6), the point B\displaystyle B has coordinates (6,8)\displaystyle (6,8) and the point C\displaystyle C has coordinates (4,2)\displaystyle (4,2).
(a) Find the exact length of
(i) AB\displaystyle AB,
(ii) BC\displaystyle BC,
(iii) AC\displaystyle AC.
(4)
(b) Find the size of each angle of triangle ABC\displaystyle ABC in degrees.
(3)
The points A\displaystyle A, B\displaystyle B and C\displaystyle C lie on a circle with centre P\displaystyle P.
(c) Find the coordinates of P\displaystyle P.
(2)
(d) Find the exact length of the radius of the circle in the form a\displaystyle \sqrt{a}, where a\displaystyle a is an integer.
(2)